Triple concentric conductor system



April 19, 1932. E. GREEN TRIPLE CONCENTRIC CONDUCTOR SYSTEM Filed Jan. 50, 1930 INVENTOR Ell Gneen/ W ATTORNEY Patented Apr. 19, 1932 v UNITED STATES PATENT OFFICE ESTILL I. GREEN, OF EAST ORANGE, NEW JERSEY, ASSIGNOR TO AMERICAN TELEPHONE AND TELEGRAPH COMPANY, A CORPORATION OF NEW YORK TRIPLE CONCENTRIC CONDUCTOR SYSTEM Application filed January 30, 1930. Serial No. 424,679.

This invention relates to concentric conductor systems, and more particularly to a system in which more than two concentric conductors are employed.

It has been proposed that an arrangement M of three concentric cylindrical conductors of different sizes may be employed as a transmission medium. Where any two concentric conductors are connected so that one acts as a return for the other, due to the skin effect at high frequencies the current tends to crowd to the adjacent surfaces of the two conductors. In other words, the current flow concentrates at the inner surface of the outer of the two conductors and at the outer surface of the inner conductor. It is, therefore, possible in a triple conductor system to use the middle and inner conductors as one circuit and the middle and outer conductors as an independent circuit. At high frequencies the two circuits will be effectively separated since the currents of one circuit will flow on the inside of the middle conductor and those of the other circuit on the outside of the mid- 26 dle conductor.

The present invention is concerned with the discovery that the two independent circuits thus formed may be so constructed as to have the same attenuation and that such at- 30 tenuation will have a minimum value for any given diameter of the outside conductor if the concentric conductors have certain diameter ratios.

The invention mill now be more fully understood from the followingdescription when read in connection with the accompanying drawing, Figure 1 of which shows schematically the general arrangement of a concentric conductor system of three conductors, and Fig. 2 of which is a cross-section of the triple conductor system to show the diameter relations.

Let us consider a triple conductor system comprising an inner conductor 2', a middle conductor m and an outer conductor 0 coaxially arranged as shown in Figs. 1 and 2. The propostion is to use the middle and inner conductors, for example, as one circuit, and the middle and outer conductors as another. This is rendered possible due to the skin effect which, as already stated, causes the currents of one circuit to flow at high frequencies on the inside of the middle conductor and the currents of the other circuit to flow on the outside surface of said conductor, the return currents of the two circuits flowing at the inner surface of the outer conductor and the outer surface of the inner conductor, respectively.

The diameter of the outer conductor is usually determined by practical considerations, such as the size of conduit ducts or of overhead cable rings, and likewise the thickness of the conductor walls will ordinarily be determined by mechanical considerations. It is desirable that the attenuation of the circuit derived from the middle and inner con ductors should be the same as that of the circuit derived from the middle and outer conductors, since this condition would give equal 10 repeater spacings and equal frequency ranges on the two circuits. Assuming the foregoing conditions, let us determine the diameter relations for the triple conductor system which will make the attenuation of the two circuits; equal and make this attenuation a minim for a fixed total amount of conductor mate rial.

Let a and b be the inner and outer radii re spectively of the inner conductor 2', c and d the corresponding radii of the middle conductor m and e and the inner and outer radii of the outer conductor 0. Bearing in mind that under the assumed conditions the current flow is concentrated at the adjacent sur- 35 faces of the conductors constituting a given conducting system, the following formulae may be used at high frequencies for the conducting system comprising the middle conductor m and the outer conductor 0:

Resistance of middle conductor Rm: Kr; 1)

Resistance of outer conductor Linear inductance= where the mbol denotes approximate equality. e then have L=K log a (3) I M%21rt(b+c+a) (12) mear capac1 y or, if

0== K as log; 4) l M bein assumed constant where K, K and K are constants and F is the frequency. It will be noted that the outer b 0+ e 10 radius of the outer conductor and the inner wh radius of the middle conductor do not appear 0 Km in the formulae. I 1 (14) The attenuation at high frequencies is: s

Since (1 is approximately equal to c, Equa- R Z G I tion (8) may be rewritten d1=- 'l' 50 3)? (15) where R, L, C and G are the hnear resistance, 1 inductance, capacity and leakage inductance, c 11 respectively. Let us assume, first, that air Whlch from (14) becomes insulation is employed between the conduc- K 6 e c 1 tors and that G=0. We have, then: a +1)(1+; (16) 10 Z R,.+R, 5 p g 6 00 '2 Z 2 \{Z or, letting Substituting the values given by Equations =2 and =E 1 to (4 inclusive, in Equation 6 we c b obtain: K 1 1 1X-+1) 17 a1=KJF( +1) 5! (7) 10 w H 2/ e11- 2 d 0 K1 5) Likewise, it is found that Letting a,= +1 e+ 1) 1 (18) K a: log a: IT, Since the two attenuations a and a; are to be equal, we find that Equation (7) becomes: 1 m5 1 1 1 :c'+1 11 (19) 8 on Ku/F(z+ log g 3 y g The problem is to find the values of a: and I Similarly, the attenuation of the circult y which ti f 9 and make the attemm, formed y the Huddle and 1111191 conductors tion a minimum. A mathematical solution y be expressed: is difiicult. A satisfactory solution may be 1 1 1 secured, however, by approximate methods. ,=K, JF (9) A range of values maybe assumed for :z' and b l g for each of these a corresponding value of b y which satisfies (19) may be found either graphically or by successive computations The Qmount of conductor mammal P m from tables. Upon substituting these diflerlength 151 ent pairs of values for m and y in Equation 16o (18) the particular values which give minia2) +w d2 02) +1r f2 e2) (10) mum attenuation are found. These values Let us assume that the thickness of the three are conductors is the same, or 1n other words, that z 234.18

b-a=dc=fe=t=constant (11) e Let us also assume that t is small in com- !/=E=T parison with the radii of the conductors, so that When the diameter ratios are near these ba, d=:-c and je optimal values the change of attenuation 1 mission systems will be with changing diameter ratio is not large, so

that some degree of departure from the exact values of (20) and (21) can be introduced while still keeping the attenuation a minimum for all practical purposes.

The use of insulating spacers to keep the conductors in concentric relation will have some effect upon the diameter ratios required for minimum attenuation, but these insulators can be spaced at fairly great intervals, and their efiect will then be practically negligible. Likewise it should be noted that while certain simplifying assumptions have been made in determining the optimal diameter ratios, reasonable modifications can be made in these assumptions without changing the validity of the above conclusions.

It will be obvious that the general principles herein disclosed may be embodied in many other organizations widelydifferent from those illustrated without departing from the spirit of the invention as defined in the followmg'claims.

What is claimed is:

1. A triple conductor system comprising inner, middle and outer conductors concentrically arranged with the middle and outer conductors constituting one transmission system and the inner and middle conductors constituting an independent transmission system, the diameters of the three conductors being so related that for a given amount of conductor material and a given size of outer con ductor the attenuations of the two independent transmission systems wil be a minimum.

2. A triple conductor system comprising inner, middle and outer conductors concentrically arranged with the middle and outer conductors constituting one transmission system and the inner and middle conductors constituting an independent transmission s stem, the diameters of the three conductors b ing so related that for a given amount of conductor material and a given size of outer conductor the attenuations of the two independent transmission systems will be the same and have a minimum value.

3. A triple conductor system comprising inner middle and outer conductors concentrically arranged with the middle and outer conductors constituting one transmission system and the inner and middle conductors constitutin an independent transmission system, the ratio of the inner diameter of the outer conductor to the outer diameter of the middle conductor, and the ratio of the inner diameter of the middle conductor to the outer diameter of the inner conductor, being such thatfor a given amount of conductor material and a given size of outer conductor the attenuation for the two independent transa minimum.

4. A tri 1e conductor-system comprising conductors constituting one transmission system and the inner and middle conductors constituting an independent transmission system, the ratio of the inner diameter of the outer conductor to the outer diameter of the middle conductor, and the ratio of the inner diameter of the middle conductor to the outer diameter of the inner conductor, being such that for a given amount of conductor materialand a given size of outer conductor the attenuations of the two independent transmission systemswill be equal and will have minimum values.

5. A triple conductor system comprising inner, middle and outer conductors concentrically arranged with the middle and outer conductors constituting one transmission system and the inner and middle conductors constituting an independent transmission system, the ratio of the inner diameter of the outer conductor to the outer diameter of the middle conductor being substantially 1.57

and the ratio of the inner diameter of the middle conductor to the outer diameter of the inner conductor being substantially 4.18.

6. A triple conductor system comprising inner, middle and outer conductors concentrically arranged, with the middle and outer conductors comprising one transmission circuit and the inner and middle conductors comprising an independent transmission circuit, the ratio of the inner diameter of the outer conductor to the outer diameter of the middle conductor being substantially 1.6, and the ratio of the inner diameter of the middle conductor to the outer diameter of the inner conductor being such as to make the attenuation of the inner circuit substantially the same as that of the outer circuit.

In testimony whereof, I have signed my name to this specification this 29th day of January, 1930.

. ESTILL I. GREEN.

inner mid e and outer conductors concen- 

